Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 10 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.31117644849206148748589.1	x^20 - 5x^19 + 12x^18 - 17x^17 + 21x^16 - 25x^15 + 43x^14 - 63x^13 + 89x^12 - 93x^11 + 103x^10 - 93x^9 + 89x^8 - 63x^7 + 43x^6 - 25x^5 + 21x^4 - 17x^3 + 12x^2 - 5x + 1	\( 29^{5}\cdot 79^{8} \)	20T436	Trivial
20.0.26169939318182371097563349.1	x^20 - x^19 + x^18 + x^17 + 7x^16 + 5x^15 + 3x^14 + 10x^13 + 17x^12 + 48x^11 + 34x^10 + 48x^9 + 69x^8 + 113x^7 + 126x^6 + 66x^5 + 31x^4 - 12x^3 + 4x^2 - 5x + 1	\( 29^{7}\cdot 79^{8} \)	20T436	$[2]$ (GRH)
20.4.194205221503895574339943949.1	x^20 - x^19 - 3x^17 - 16x^16 + 81x^15 - 29x^14 - 152x^13 + 171x^12 + 465x^11 - 145x^10 - 859x^9 + 29x^8 + 644x^7 - 391x^6 - 388x^5 + 317x^4 - 211x^3 + 123x^2 - 56x + 1	\( 29^{5}\cdot 79^{10} \)	20T436	Trivial (GRH)
20.8.248239988522131354693148893.1	x^20 - 8x^19 + 29x^18 - 61x^17 + 76x^16 - 55x^15 - 39x^14 + 189x^13 - 332x^12 + 413x^11 - 447x^10 + 167x^9 + 177x^8 - 363x^7 + 550x^6 - 356x^5 - 4x^4 + 90x^3 - 25x^2 - 2x + 1	\( 13^{5}\cdot 401^{8} \)	20T436	Trivial (GRH)
20.4.32629215565401186630200459264.1	x^20 + x^18 + 4x^16 - 99x^14 - 192x^12 - 491x^10 - 412x^8 + 870x^6 + 3277x^4 + 19343x^2 + 24389	\( 2^{20}\cdot 29^{5}\cdot 79^{8} \)	20T436	Trivial (GRH)
20.8.41952558060240198943142162917.2	x^20 + 7x^18 - 4x^16 - 57x^14 + 31x^12 - 563x^10 - 407x^8 + 6239x^6 - 6205x^4 + 234x^2 + 13	\( 13^{7}\cdot 401^{8} \)	20T436	Trivial (GRH)
20.4.39917238394347243966013035143293.3	x^20 - 8x^19 + 28x^18 - 71x^17 + 115x^16 + 39x^15 - 838x^14 + 2849x^13 - 5828x^12 + 6380x^11 + 3122x^10 - 32134x^9 + 80489x^8 - 120236x^7 + 96732x^6 + 38489x^5 - 284352x^4 + 543530x^3 - 660153x^2 + 558756x - 241893	\( 13^{5}\cdot 401^{10} \)	20T436	$[2]$ (GRH)
20.4.6746013288644684230256202939216517.3	x^20 - 6x^19 + 8x^18 - 15x^17 + 49x^16 - 26x^15 - 374x^14 + 774x^13 + 3353x^12 + 8269x^11 + 714x^10 - 46770x^9 - 121638x^8 - 182475x^7 - 190983x^6 - 119310x^5 - 26897x^4 + 7860x^3 + 6695x^2 + 6057x + 2511	\( 13^{7}\cdot 401^{10} \)	20T436	Trivial (GRH)
20.20.1064302799514018391410011360416915869649.1	x^20 - 9x^19 - 34x^18 + 514x^17 - 281x^16 - 9650x^15 + 18041x^14 + 80127x^13 - 215841x^12 - 303918x^11 + 1139768x^10 + 387555x^9 - 2941138x^8 + 485980x^7 + 3639822x^6 - 1676891x^5 - 1746811x^4 + 1208121x^3 + 16821x^2 - 93015x + 11259	\( 17^{5}\cdot 257^{5}\cdot 401^{8} \)	20T436	Trivial (GRH)
20.20.1923057841875192078295334939374681428125.1	x^20 - 6x^19 - 73x^18 + 400x^17 + 1991x^16 - 10140x^15 - 26430x^14 + 125469x^13 + 190243x^12 - 838980x^11 - 750656x^10 + 3181262x^9 + 1469249x^8 - 6919514x^7 - 821136x^6 + 8254333x^5 - 1321719x^4 - 4616820x^3 + 1700525x^2 + 709315x - 328885	\( 5^{5}\cdot 19^{10}\cdot 43^{8}\cdot 97^{5} \)	20T436	Trivial (GRH)